二阶流体在旋转坐标系中的三维管道流动

就两个水平板构成的旋转系统,在磁场作用下分析二阶磁流体在其间的流动.下表面是一块可伸展的平面,上面是一块多孔的固体平板.选用合适的变换,将质量和动量的守恒方程,简化为耦合的非线性常微分方程组.应用最强大的分析技术,即同伦分析法(HAM),得到该非线性耦合方程组的级数解.结果用图形给出,并详细地讨论了无量纲参数Re,λ,Ha2,α和K2对速度场的影响.     

具有收缩表面的二阶流体驻点流动的级数解

研究具有收缩表面的边界层流动的解析解.通过相似变换,将偏微分方程简化为可用同伦分析法(HAM)求解的常微分方程.然后讨论了具有收缩表面的二维轴对称流动.     

DTM-BF方法和可渗透收缩壁面上带滑移速度的非稳态磁流体力学流动

研究了运动的粘性导电流体中可渗透收缩壁面上非稳态磁流体边界层流动,利用解析和数值方法对问题进行了研究,并考虑了壁面速度滑移的影响．提出了一个新的解析方法（DTM-BF）,并将其应用于求解带有无穷远边界条件的非线性控制方程的近似解析解．对所有的解析结果和数值结果进行了对比,结果显示两者非常吻合,从而证明了DTM-BF方法的有效性．另外,对不同的参数,得到了控制方程双解和单解的存在范围．最后,分别讨论了滑移参数、非稳态参数、磁场参数、抽吸/喷注参数和速度比例参数对壁面摩擦、唯一解速度分布和双解速度分布的影响．     

生物磁粘弹性流体的流动:应用动脉电磁过热评估血液的流动,癌症治疗进程

利用生物磁流体动力学(BFD)原理,在生物磁流体经由遭受磁场作用的多孔介质时,研究其流动的基本理论.所研究流体的磁化强度随温度而变化.流体被认为是非Newton流体,其流动由二阶梯度流体方程所控制,并考虑了流体的粘弹性效应.假设管道壁是能够伸展的,管壁表面的速度与到坐标原点的纵向距离成正比.首先将问题简化为包括7个参数的、耦合的非线性微分方程组的求解.将血液看作生物磁流体,并用上述方法分析,目的是计算某些血液的流动参数,并配以适当的数值方法,导数用差分格式近似.计算结果用图形给出,从而在磁场作用下,得到过热状态中关系血液的、血流动力学流动的理论预测.结果清楚地表明,在电磁过热治疗进程期间,磁偶极子对动脉中血液流动特征的影响起着重大作用.该研究引起了临床医学的关注,其结果有益于癌症病人采用电磁过热的治疗.     

可渗透收缩薄膜引起的三维

研究可渗透收缩薄膜上的不稳定粘性流动.通过相似变换得到相似方程.在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等.结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解.     

关于N.A.Menger PN-空间中概率收缩偶与非线性方程组的解的注记

引进了(Φ,Δ)-型概率收缩偶的概念,它简化并减弱了张石生给出的概率收缩偶的定义。在N.A.Menger PN-空间中研究了具有这类概率收缩偶的非线性算子方程组的解的存在性与唯一性问题。改进并推广了M.Altman,A.C.Lee,W.J.Padgett,张石生等人的相应结果。     

纳米流体在非线性伸展面上粘性流动及其热交换时的相似解

当含金属颗粒的粘性流体(即纳米流体)流过非线性伸展平面时,分析其边界层流动及其热交换.假设伸展速度是到原点距离的幂函数.将偏微分的控制方程及其相应的边界条件,简化为耦合的非线性常微分方程及其相应的边界条件.数值地求解所得到的非线性常微分方程.讨论了各相关参数(即Eckert数Ec,纳米颗粒的固体体积率和非线性伸展参数n)对问题结果的影响,并与先前文献所报道的结果进行了对比.研究了不同类型的纳米颗粒.发现纳米流体的流动特性随着纳米颗粒类型的改变而变化.     

应用逐次Taylor级数线性化法在多孔伸展界面上求解高对流Maxwell流体的磁流体动力学流动

研究不可压缩的高对流Maxwell(UCM)流体,在多孔伸展界面上作磁流体动力学(MHD)的边界层流动.利用相似变换将控制的偏微分方程,变换为非线性常微分方程.采用逐次Taylor级数线性化方法(STLM)求解该非线性问题.对所显现的参数完成速度分量的计算,介绍了表面摩擦因数的数值结果,并分析了问题所显现参数的变化.     

热辐射对粘性流体流过多孔非线性收缩平面时的MHD流动和热传导的影响

研究热辐射对多孔非线性收缩平面上磁流体动力学(MHD)流动和热传导的影响.假设收缩平面的速度和横向磁场,按离原点距离的幂函数而变化;又假设粘性按与其有关的温度的反函数变化,热传导率按温度的线性函数变化.通过广义相似变换,将偏微分方程的控制方程,简化为耦合的非线性常微分方程,然后通过有限差分法进行数值求解.在不同的参数取值下,得到速度和温度分布,以及多孔平面上表面摩擦因数和热传导率的数值结果.     

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.     

朝向产热或吸热伸展平面的MHD驻点流动

分析了微极流体朝向加热伸展平面的磁流体动力学(MHD)驻点流动,考虑了粘性耗散和内部产热/吸热对流动的影响.讨论了指定表面温度(PST)和指定热通量(PHF)两种情况,采用同伦分析方法(HAM)求解边界层流动和能量方程.通过图表的显示,研究了感兴趣物理量的变化.注意到高伸展参数时解的存在与外加应用磁场密切相关.     

Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space

This article looks into the unsteady rotating magnetohydrodynamic (MHD) flow of an incompressible second grade fluid in a porous half space. The flow is induced by a suddenly moved plate in its own plane. Both the fluid and plate rotate in unison with the same angular velocity. Analytic solution of the governing flow problem is obtained by using Fourier sine transform. Based on the modified Darcy's law, expression for velocity is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. Several existing solutions of Newtonian fluid have been also deduced as limiting cases.     

Three-dimensional rotating flow induced by a shrinking sheet for suction

Series solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet is obtained by a homotopy analysis method (HAM). The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Similarity solutions of coupled non-linear ordinary differential equations resulting from the momentum equation are obtained. Convergence of the obtained solutions is ensured by the proper choice of auxiliary parameter. Graphs are sketched and discussed for various emerging parameters on the velocity field. The variations of the wall shear stress f″(0) and ?g′(0) are also tabulated and analyzed.     

Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet

The magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet is examined analytically. The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants to handle the condition at infinity. The numerical solutions agree very well with the results by the homotopy analysis method.     

可渗透壁面上Falkner-Skan磁流体动力学流动的近似解

研究了可渗透壁面上Falkner-Skan磁流体动力学（MHD）边界层流动问题．利用结合了微分变换法（DTM）和Padé近似的DTM-Padé方法,得到了边界层问题的近似解和壁摩擦因数值．通过建立一个迭代程序,边界层问题的近似解被表示为幂级数的形式,而且以图和表形式对不同参数下的近似解结果与打靶法得到的数值结果进行了对比,近似解和数值解结果高度吻合,从而验证了所得问题近似解和结论的可靠性和有效性．并且,对求得的边界层问题近似解结果进行了讨论,分析了不同物理参数对边界层流动的影响．     

On a perturbation treatment of a model for MHD viscous flow

We discuss the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet. We propose an accurate numerical solution and derive simple analytical expressions. Our results suggest that a recent perturbation treatment of the same problem exhibits a pathological behaviour and conjecture its probable cause.     

Closed-form exact solutions of MHD viscous flow over a shrinking sheet

In this paper, the magnetohydrodynamic (MHD) flow over a shrinking sheet is solved analytically. The solution is given in a closed-form equation and is an exact solution of the full governing Navier–Stokes equations for the problem. Interesting solution behavior is observed with multiple solution branches for certain parameter domain.     

Unsteady MHD two-phase Couette flow of fluid–particle suspension

The problem of two-phase unsteady MHD Couette flow between two parallel infinite plates has been studied taking the viscosity effect of the two phases into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving plate. The novelty of this study is that we have obtained the solution of the unsteady flow using the Laplace transform technique, D’Alemberts method and the Riemann-sum approximation method. The solution obtained is validated by assenting comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical result for the velocity of both phases based on the semi-analytical solutions are presented and discussed. A parametric study of some of the physical parameters involved in the problem is conducted. The skin friction for both the fluid and the particle phases decreases with time on both plates until a steady state is reached, it is also observed to decrease with increase in the particle viscosity on the moving plate while an opposite behaviour has been noticed on the stationary plate.     

Analytical solution of hydromagnetic flow with Hall effect over a surface stretching with a power‐law velocity

The nonlinear magnetohydrodynamic (MHD) flow problem with Hall current caused by stretching surface having power law velocity distribution is solved by employing homotopy analysis method (HAM). Perturbation solution of stream function, the expression of skin friction coefficient and graphical results in absence of Hall current (Chiam, Int J Eng Sci 33 (1995), 429) are recovered as the limiting cases. It is found that unlike the solution obtained by Chiam (1995), the present results are valid for weak and large magnetic parameters. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 937–959, 2011